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Homework_Assignment_2 - Homework Assignment 2(1 For a...

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Homework Assignment 2: (1) For a certain type of policy an insurance company divides its claims into two classes, minor and major. Last year 90% of the policyholders filed no claims, 9 percent filed minor claims and 1 percent filed major claims. The amounts of the minor claims were uniformly distributed over (0,1000), and the major claims were uniformly distributed over (1000,10000). Let X = the amount paid to a randomly selected policyholder. Find F(x) for 0 x 10000. Ans: F(0) = .90 F(x) = .90 + .09x/1000 for 0 < x 1000 F(x) = .99 + .01(x – 1000)/9000 for 1000 < x 10000 (2) A random loss has the following probability distribution: Amount of Loss: 0 1 2 3 5 6 7 9 Probability : .5 .1 .1 .1 .1 .05 .025 .025 An insurer will pay nothing if the loss is 2, and will pay the loss minus 2 if the loss is > 2, but the maximum payment will be 4. Find the variance of the payment. (Ans 1.96) (3) An insurance policy reimburses a loss up to a benefit limit of 10. The policyholder’s loss, X, follows a distribution with density function:
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